In the given circuit, for voltage {V}_{ {y}} to be zero, the value of \beta should be ______________. (Round off to 2 decimal places).

GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 23 of 65

Marks: +1, -0

In the given circuit, for voltage

{V}_{ {y}}

to be zero, the value of

β

should be ______________. (Round off to 2 decimal places).

Solution:

Given,

{V}_{ {y}}=0

Apply, KCL at node (1),

\;{V_{x}-6}/{1}+\;{V_{x}}/{4}+\;{V_{x}-0}/{2}=0

4 {V}_{ {x}}-24+ {V}_{ {x}}+2 {V}_{ {x}}=0

{V}_{ {x}}=\;{24}/{7} {V}

Apply, KCL at node

(2)

\;{V_{x}}/{2}+2=\;{0-β V_{x}}/{3}

\;{3 V_{x}}/{2}+6=-β V_{x}

\;{36}/{7}+6=-\;{24}/{7} β

β=-\;{78}/{24}

β=-3.25

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